An Intuitionistic Set-theoretical Model of Fully Dependent CC{\omega}

Masahiro Sato; Jacques Garrigue

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arXiv · 2010.12504

An Intuitionistic Set-theoretical Model of Fully Dependent CC{\omega}

Masahiro Sato·Jacques Garrigue

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Abstract

Werner's set-theoretical model is one of the simplest models of CIC. It combines a functional view of predicative universes with a collapsed view of the impredicative sort Prop. However this model of Prop is so coarse that the principle of excluded middle holds. Following our previous work, we interpret Prop into a topological space (a special case of Heyting algebra) to make the model more intuitionistic without sacrificing simplicity. We improve on that work by providing a full interpretation of dependent product types, using Alexandroff spaces. We also extend our approach to inductive types by adding support for lists.

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Masahiro Sato, Jacques Garrigue. 2020-10-23. An Intuitionistic Set-theoretical Model of Fully Dependent CC{\omega}. https://arxiv.org/abs/2010.12504

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